Question

An investor wants to find the duration of a(n) 10-year, 9% semiannual pay, noncallable bond that's currently priced in the market at $937.69 to yield 10%. Using a 200 basis point change in yield, find the effective duration of this bond (Hint use Equation 11.11) The new price of the bond if the market interest rate decreases by 200 basis points (or 2%) is $ (Round to the nearest cent.) The new price of the bond if the market interest rate increases by 200 basis points (or 2%) is $(Round to the nearest cent.) The effective duration of the bond is (Round to two decimal places.)

Answer 1

Duration:
Duaration = Sum [ Weight * Year ]

Period	CF	PVF @5%	Disc CF	Weight	Wt * Period
1	$      45.00	0.9524	$   42.86	0.0457	0.0457
2	$      45.00	0.9070	$   40.82	0.0435	0.0871
3	$      45.00	0.8638	$   38.87	0.0415	0.1244
4	$      45.00	0.8227	$   37.02	0.0395	0.1579
5	$      45.00	0.7835	$   35.26	0.0376	0.1880
6	$      45.00	0.7462	$   33.58	0.0358	0.2149
7	$      45.00	0.7107	$   31.98	0.0341	0.2387
8	$      45.00	0.6768	$   30.46	0.0325	0.2599
9	$      45.00	0.6446	$   29.01	0.0309	0.2784
10	$      45.00	0.6139	$   27.63	0.0295	0.2946
11	$      45.00	0.5847	$   26.31	0.0281	0.3086
12	$      45.00	0.5568	$   25.06	0.0267	0.3207
13	$      45.00	0.5303	$   23.86	0.0255	0.3309
14	$      45.00	0.5051	$   22.73	0.0242	0.3393
15	$      45.00	0.4810	$   21.65	0.0231	0.3463
16	$      45.00	0.4581	$   20.62	0.0220	0.3518
17	$      45.00	0.4363	$   19.63	0.0209	0.3559
18	$      45.00	0.4155	$   18.70	0.0199	0.3589
19	$      45.00	0.3957	$   17.81	0.0190	0.3608
20	$      45.00	0.3769	$   16.96	0.0181	0.3617
20	$ 1,000.00	0.3769	$ 376.89	0.4019	8.0387
Duration in Periods	13.3632
No. of periods per anum	2.0000
Duration in Years	6.6816

Modified duaration :
Modified duration = Duration / [ 1 + YTM ]
It specifies% change in Price in opposite direction due to 1% change in YTM.

= 6.6816 / 1.10

= 6.0742

i.e 1% change in YTM leads to 6.0742% chnage in price in opposite direction

2% change leads to 12.15% [ 6.0742* 2 ]

Price if Int dec by 2% :

= Old price * ( 1 + 0.1215 )

= 937.69 * 1.1215

= 1051.62

Price if Int inc by 2% :

= Old price * ( 1 - 0.1215 )

= 937.69 * 0.8785

= 855.39

Pls do rate, if the answer is correct and comment, if any further assistance is required.